Auto-bidding plays an important role in online advertising and has become a crucial tool for advertisers to meet their performance objectives and for advertising platforms to optimize the efficiency of ad delivery. Advertisers employing auto-bidding only need to express high-level goals and constraints, and leave the bid optimization problem to the advertising platforms. As auto-bidding has changed the bidding language and the way advertisers participate in the ad auction, fundamental investigation into mechanism design for auto-bidding environment should be made to study the interaction of auto-bidding with advertisers. In this paper, we formulate the general problem of incentive mechanism design for ROI-constrained auto-bidding, and carry out analysis of strategy-proof requirements for the revenue-maximizing and profit-maximizing advertisers.